Cartesian to Polar Coordinates: A Step-by-Step Guide

5/3/2026

6 min read

In this article, we will learn how to convert Cartesian coordinates to Polar coordinates

Explanation

Cartesian coordinates are a way to describe points in a 2D plane using x and y values. Polar coordinates are a way to describe points in a 2D plane using radius (r) and angle (θ)

Formula

r = √(x² + y²)
θ = atan2(y, x)

Example

For example, to convert (3, 4) to Polar coordinates, we use the formula: r = √(3² + 4²) = √(9 + 16) = √25 = 5, θ = atan2(4, 3) = 0.927 radians

How to use the related calculator

To use this tool, simply enter the x and y coordinates in the input fields and click the 'Calculate' button. The tool will then display the Polar coordinates

Try the related calculator

Open tool

FAQ

What are the benefits of using Polar coordinates?

Polar coordinates are useful in many applications, such as navigation, physics, and engineering

How do I convert Polar coordinates back to Cartesian coordinates?

To convert Polar coordinates back to Cartesian coordinates, you can use the formulas: x = r * cos(θ), y = r * sin(θ)